Definable functions in the simply typed lambda-calculus
| dc.creator | Zakrzewski, Mateusz | |
| dc.date | 2007-01-04 | |
| dc.date.accessioned | 2026-07-07T07:38:31Z | |
| dc.date.available | 2026-07-07T07:38:31Z | |
| dc.description | It is a common knowledge that the integer functions definable in simply typed lambda-calculus are exactly the extended polynomials. This is indeed the case when one interprets integers over the type (p->p)->p->p where p is a base type and/or equality is taken as beta-conversion. It is commonly believed that the same holds for beta-eta equality and for integers represented over any fixed type of the form (t->t)->t->t. In this paper we show that this opinion is not quite true. We prove that the class of functions strictly definable in simply typed lambda-calculus is considerably larger than the extended polynomials. Namely, we define F as the class of strictly definable functions and G as a class that contains extended polynomials and two additional functions, or more precisely, two function schemas, and is closed under composition. We prove that G is a subset of F. We conjecture that G exactly characterizes strictly definable functions, i.e. G=F, and we gather some evidence for this conjecture proving, for example, that every skewly representable finite range function is strictly representable over (t->t)->t->t for some t. | |
| dc.description | Submitted to TLCA 2007 | |
| dc.identifier | https://arxiv.org/abs/cs/0701022 | |
| dc.identifier | http://arxiv.org/abs/cs/0701022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121114 | |
| dc.subject | Logic in Computer Science | |
| dc.title | Definable functions in the simply typed lambda-calculus | |
| dc.type | text |